Question 1

Which of the following relations is a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4)\}$$

Question 2

Given the equation $$y = -2x + 10$$, is this a function? If so, what is $$f(3)$$?

Accepted Answer

Yes, $$f(3) = 4$$

Question 3

Which graph passes the Vertical Line Test and represents a function?

Accepted Answer

A parabola opening upwards

Question 4

What is the domain of the function $$f(x) = \sqrt{x+4}$$?

Accepted Answer

$$[-4, \infty)$$

Question 5

Find the domain of $$f(x) = \frac{1}{x^2$ - 5x + 6}.$$

Accepted Answer

$$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$$

Question 6

Which of the following equations is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 25$

Question 7

Given the graph of $$f(x)$$ with domain $$[-4, 5]$$ and range $$[-2, 6]$$, which interval notation correctly expresses the range?

Accepted Answer

$$[-2, 6]$$

Question 8

If $$f(x) = \sqrt{x}$$, what is the restriction on $$x$$ for the domain?

Accepted Answer

$$x \geq 0$$

Question 9

A function $$f is $$defined by $$f(x) = x^2$ - 4x + 3. $$What is $$f(-2)$$?

Accepted Answer

$$f(-2) = 15$$

Question 10

Which of the following is the correct interval notation for the domain of $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 11

Given the relation $$\{(1,2), (2,3), (3,4), (2,5)\}$$, is this a function?

Accepted Answer

No, because the input 2 maps to two different outputs

Question 12

If the graph of a relation fails the Vertical Line Test, what does this mean?

Accepted Answer

The relation is not a function

Question 13

What is the range of $$f(x) = x^2$ for x$ in $$[-2, 3]$$?

Accepted Answer

$$[0, 9]$$

Question 14

Which of the following is the correct set builder notation for the domain of $$f(x) = \sqrt{x+4}$$?

Accepted Answer

$$\{x \mid x \geq -4\}$$

Question 15

For the function $$f(x) = \frac{2x+1}{x-3}$$, what value of $$x is $$excluded from the domain?

Accepted Answer

$$x = 3$$

Question 16

If $$f(x) = \sqrt{x-2}$$, what is $$f(6)$$?

Accepted Answer

$$f(6) = 2$$

Question 17

Which of the following is NOT a valid interval notation for a domain?

Accepted Answer

$$[5, -2]$$

Question 18

Given $$f(x) = x^2$ and g(x) = x + 2$, what is f(g(2$$))$$?

Accepted Answer

$$f(g(2)) = 16$$

Question 19

If $$f(x) = \frac{1}{x}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 20

Which of the following statements about functions is TRUE?

Accepted Answer

A function assigns exactly one output to each input

Relations, Functions, and Domain & Range in College Algebra

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